A080050 Primes p such that 2^p-1 and the p-th Fibonacci number have a common factor. Prime terms of A074776.

11, 8501, 10867, 13109, 14633, 15401, 17657, 19211, 19541, 22481, 24359, 25243, 26111, 29411, 30851, 34961, 36007, 42443, 43331, 45523, 46187, 46601, 47591, 50411, 57251, 58027, 61001, 62921, 63131, 64123, 70639, 74293, 76919, 78941

Offset

1,1

Comments

This sequence is a subsequence of A074776 and all multiples k*p of this sequence are in A074776, i.e., they satisfy gcd(2^(k*p)-1, Fibonacci(k*p)) > 1. This was proved by Anthony Mendes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

89 divides both 2^11-1=2047 and Fibonacci(11)=89, so 11 is in the sequence.

Mathematica

Select[Prime[Range[8000]], GCD[2^#-1, Fibonacci[#]]>1&] (* Harvey P. Dale, Mar 16 2020 *)

Prog

(PARI) forprime(p=1, 10^5, if(gcd(2^p-1, fibonacci(p))>1, print(p))).

Crossrefs

Cf. A000045, A030426, A074776, A079506, A079670.

Common factors are in A080051.

Sequence in context: A214183 A214234 A320984 * A067254 A099806 A227063

Adjacent sequences: A080047 A080048 A080049 * A080051 A080052 A080053

Keyword

nonn

Author

Ralf Stephan, Jan 22 2003

Status

approved